🎭 The costume trick
One number, three costumes
A half, 0.5 and 50% look like three different numbers, but they’re all the same amount.
At school, fractions, decimals and percentages are usually taught as three separate topics.
They often turn up in different chapters of the book.
½, 0.5 and 50% are the same number written in three different ways.
Start here
Three ways to write the same amount
This flower is exactly half open, and you can write that in three ways that are all correct. A fraction, a decimal and a percentage are three names for the same amount.
Your turn: drag the bar below. Slide it anywhere between nothing and the whole thing, and you’ll see all three names change together and always match.
All three show the same amount, and none of them is more “real” than the others.
Nearly everyone makes this next mistake at some point.
Forty-five is bigger than five, so it seems 0.45 must be bigger than 0.5.
Decide what you think before you scroll on.
The trap
0.45 looks bigger than 0.5
Forty-five is bigger than five in ordinary counting, so 0.45 feels like the bigger number. Pick an answer first (no peeking), then check it.
0.5 vs 0.45
One word explains how all three are linked.
Per cent is Latin for “out of a hundred”.
The why
Everything counts out of a hundred
A percentage is a fraction with 100 on the bottom, and a decimal’s first two places count those same hundredths. Your turn: tap or drag across this grid to paint squares and you’ll see all three show the same amount.
0 of 100 painted
0
0
0%
Doing the sums
Turning any score into a percentage
Tests are often marked “out of 50” or “out of 20”. To turn a score into a percentage, make the bottom number 100 and do the same thing to the top. Change the numbers and you’ll see why the tempting answer is wrong.
Some fractions are harder to write as decimals.
One of them can never be written as a decimal that ends.
Write a third as a decimal and the 3s go on forever.
The odd one out
A decimal that never ends
A half, a quarter, a fifth and a tenth all turn into neat decimals that end. ⅓ is different: you can write it exactly as a fraction, but as a decimal it never finishes. Your turn: tap “a third” below and watch what the decimal does.
A third is different. As a fraction it’s exactly 1/3, but as a decimal the 3s go on forever: 0.333…
Once you know how the three are linked,
three chapters of the book become one.
A half, 0.5 and 50% are the same amount written in different ways.
One more thing
You’ll see these amounts written different ways all the time. A phone battery at 50% is half charged. A sale with 25% off takes a quarter off the price. A 70% chance of rain can also be written as 0.7.
If someone tells you 0.45 is bigger than 0.5 because forty-five is bigger than five, show them how to check: write both with two digits after the point (0.45 and 0.50) and compare the hundredths.